Issue |
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
|
|
---|---|---|
Page(s) | 1229 - 1261 | |
DOI | https://doi.org/10.1051/m2an/2024020 | |
Published online | 15 July 2024 |
Optimized Schwarz waveform relaxation method for the incompressible Stokes problem
1
Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539, Institut Galilée, 99 Av. J.-B. Clément, 93430 Villetaneuse, France
2
Université Paris-Saclay, CEA, Service de Génie Logiciel pour la Simulation, 91191 Gif-sur-Yvette, France
* Corresponding author: pascal.omnes@cea.fr
Received:
24
May
2023
Accepted:
13
March
2024
We propose and analyse the optimized Schwarz waveform relaxation (OSWR) method for the unsteady incompressible Stokes equations. Well-posedness of the local subdomain problems with Robin boundary conditions is proved. Convergence of the velocity is shown through energy estimates; however, pressure converges only up to constant values in the subdomains, and an astute correction technique is proposed to recover these constants from the velocity. The convergence factor of the OSWR algorithm is obtained through a Fourier analysis, and allows to efficiently optimize the space-time Robin transmission conditions involved in the OSWR method. Then, numerical illustrations for the two-dimensional unsteady incompressible Stokes system are presented to illustrate the performance of the OSWR algorithm.
Mathematics Subject Classification: 65M55 / 35K45 / 76D07 / 65M12 / 65M22 / 65B99
Key words: Unsteady incompressible Stokes system / space-time domain decomposition / optimized Schwarz waveform relaxation / Robin transmission conditions / correction technique for the pressure
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.